Preliminary list of abstracts

Note: We are using the fantastic MathJax JavaScript library to typeset the mathematics on this web page. You can right-click on a formula to zoom in or to select the rendering engine you like (all under 'Settings'). Under Firefox the default renderer turns out to be MathML (which is quick), but you might prefer the HTML-CSS renderer for more faithful LaTeX rendering. If you encounter any problems with this setup: then please email us!

Click here to go back to the list of abstracts.

Observations on alternating least squares
Mon, 14:25--14:50
  • Mohlenkamp, Martin (Mathematics, Ohio University, United States)

Approximating a multidimensional object by a sum of separable objects is an effective way to bypass the curse of dimensionality. The simplest, most robust, and most common algorithm to do so is Alternating Least Squares (ALS). We observe that ALS can be viewed as alternately setting partial gradients to zero or as alternately performing orthogonal projections. These dual perspectives allow us to analyze the convergence of ALS. For example, we can show that the $L^2$ norms of the increments form a sequence in $l^2$, but may not be in $l^1$. When regularization is included, we can show for example that the gradient is zero at all accumulation points.